Scanning electron microscopes (SEMs) are used to magnify small samples by scanning a focused electron beam across the surface. An SEM may also be used to obtain crystallographic information such as the size and shape of crystals or grains, the orientation of crystal lattices, and the spatial location of the crystals within a polycrystalline material.
When the electron beam in the SEM strikes the desired point upon the sample, the electrons interact with a small volume of the material and scattered electrons are diffracted by the crystal lattice so that an electron backscatter diffraction (EBSD) pattern is generated on a phosphor screen within the SEM. The screen is monitored using a low light level integrating CCD device. The CCD signal provides a digital image of the diffraction pattern for analysis by the computer which is a 2-D array of picture elements with individual intensity values. The diffraction patterns formed on the screen take the form of “Kikuchi bands” which are pairs of near straight lines. The bands show the traces of the diffracted electron beam on the phosphor plate that satisfy the Bragg conditions in the crystal. The relative spacing and angles of the bands contain information describing the orientation of the crystal under the electron beam, with respect to the beam and the phosphor screen.
The orientation of the crystal is determined by software running on the SEM computer using the Kikuchi bands in the diffraction pattern and the crystallographic information contained in a crystal structure database. This is performed using an image processing routine known as a “Hough transform” in which each pair of bands in the pattern is transformed into a spot in “Hough space”. The angular coordinates of the spot in Hough space provide the inclination angle of the Kikuchi band and the distance of the band to a selected origin. In analyzing the diffraction pattern, the software commonly selects three strong and non-coplanar Kikuchi bands in the pattern to form a triplet. The interplanar angles between each pair of the bands in the triplets are measured from the Hough transform of the pattern. They are then compared against a list of interplanar angles for the crystal calculated using the information in the crystal database. Thus, the bands are correctly indexed and the crystal orientation determined.
A problem arises when EBSD patterns are obtained using SEMs where the final (objective) electron lens for focusing the electron beam produces magnetic fields near the sample. This problem is particularly significant in “immersion-lens” SEMs where the magnetic fields in the vicinity of the sample are large. Although these magnetic fields are beneficial for image resolution, the fields distort the trajectory of the electrons emerging from the sample. EBSD patterns are distorted by these magnetic fields such that features that would appear ideally as near straight lines, are in practice curved in the EBSD pattern images obtained using an immersion-lens SEM. Therefore, analysis of such distorted EBSD pattern images by the Hough transform is impossible and this particularly limits the usefulness of immersion-lens SEMs for materials analysis.
U.S. Pat. No. 6,555,817 describes a system and method for correcting the distortion in EBSD pattern images which is based upon available empirical information. In a calibration procedure, a sample is used that would give a known pattern with nearly straight lines on an SEM which has negligible magnetic field near the sample. A distorted EBSD pattern is obtained on the immersion lens SEM and displayed on an operator display. A user input device, such as a mouse, is used by the operator to define segments following the curved Kikuchi band in the distorted EBSD pattern and the corresponding segments in the undistorted pattern. The calibration procedure calculates a series of mathematical curves to fit this segmented curved line. The mathematical curves define the amounts by which points along the user-defined curved line must be shifted in order to form a straight line. These correction parameters are saved into a pattern correction parameter data file and used to correct all subsequent patterns obtained from unknown samples.
The calibration procedure requires skill on the part of the user in identifying points along lines in the pattern and is time-consuming. Furthermore, when the field is strong, many bands in the undistorted pattern may not be visible in the distorted pattern because of a large pattern shift. Whereas the Hough transform is a well known procedure for detecting straight lines in images, the automatic detection of weak contrast lines with unknown curvature is a highly specialized and sophisticated pattern recognition problem that does not have a well known solution. The calibration procedure also requires a sufficient quantity of curved lines to be measured over the pattern to ensure that non-uniform distortion can be corrected adequately. Whereas the distortion correction obtained from a single calibration procedure should apply to all subsequent patterns obtained under identical SEM operating conditions, if the SEM accelerating voltage is changed or the specimen height is altered, then a new calibration will be required for the new conditions.